Comments - Talk
... by: nono
in the first pattern with the Xs, is it no possible to have other swordfishs with columns 2,3,4 or 2,3,6 or 3,4,6 ? why can we not work with the 2 X in column 3 ?
swordfishs will then be 3x2x3 and no 3x3x3.
merci d'avance pour la réponse
Andrew Stuart writes: I reduced the diagram to a simpler state to illustrate the pattern but I can see that could be confusing. I'd taken off the bottom two rows and only put in sufficient Xs to show one pattern but on its own, yes, other sword fishes are possible. So I have now replaced the old diagram with a full one. Refresh the page.
... by: jim
Since the 222 combination works in the swordfish. Does a 332 or 322 combination also work?
Andrew Stuart writes: Yes, all available 3s and 2s combinations
... by: Pieter, Newtown, Australia
To expand on Eric's reference to locked pairs (2011-12-2), and using the perfect 3-3-3 formation I think a different and simpler way to describe a Sword-Fish is that it is "A locked set of 3 locked-triples (sharing the same 3 rows and same 3 columns)".
The simplest 2-2-2 formation in Example 1 is "A locked set of 3 locked-pairs (sharing the same 3 rows and same 3 columns)". And as Jef points out, boxes can also be involved (if there is a locked pair linking with the other locked pairs/triples)
Also re Example 1, I think your labelling is confusing Andrew! Yes it reduces to AA, BB and CC, but to detect the Sword-Fish, the 3 pairs of 9's one needs to find are in Cols 2, 5 & 8 labelled BC, AB & AC.
Still the BEST Sudoku site on the net!
... by: Eric
I think my previous comment was a bit off-topic, since I explained X-Cycle here. This was caused due to the fact that a 2-2-2 swordfish is an X-Cycle as well.
I would like to suggest that this topic starts of with the 3-3-3 Swordfish to fully explain this subject and then focus on 2-2-2, 2-1-2, etc.
I also see great simillarity with naked pairs/triples and quads and wonder if swordfish detection for more than 3 rows or columns is useful.
... by: Eric
I think the Swordfish pattern becomes visible by connecting cells A-C, B-E and D-F. This shows 3 parallel lines that show some similarity with a Swordfish.
The Swordfish method can be explained as follows:
Statement:
Number 5 is either in the cells B+C+F or in cells A+D+E.
Proof:
- If cell B would contain numer 5, then cells B and D cannot contain 5. Therefore, on row F, cell C must contain a 5 (single candidate), and at row J, cell F must contain a 5 (again: single candidate).
- If cell A would contain number 5 than cell D+E must contain a 5 for same reason.
- At row A, number 5 can only be filled in at cell A or B, and therefore, number 5 must be present in cells B+C+F or in cells A+D+E.
Based on this statement, the pairs CE, AF and BD are locked pairs as well. Since number 5 must be in cell C or E on column 2, cell X cannot contain number 5. In column 5 cell A or F must contain number 5, and at column 9 cell B or D must contain number 5. Number 5 can thus be removed from all other cells at these columns.
Next to pairs CE, AF and BD, the following pairs are also locked pairs: AC, BE, DF.
These locked pairs are not valuable for the Swordfish strategy, but (in my opinion) these locked pairs represent the Swordfish pattern and gave name to this strategy.
... by: WLP
Re: Swordfish. Are there clues to "find' the Swordfish number? Your top/first example highlights 5 at c1, d4 and h8, and the Swordfish is based on the 5s elsewhere. Is there some significance for this? (Of course, the bottom/last example doesn't follow this approach.) I see the usefullness of this technique but spotting the correct number is difficult. Thanks!
Andrew Stuart writes: Easiest way it to highlight the each number in the solver and see if you can spot a 3-3-3 pattern in rows or columns. 3-3-3 can mean less than 2 as well, as long as you can spot a 3x3x3 grid overall. You'll also be looking for 2x2 X-Wing and you should use those first. So you're looking for the minimum number of X in one dimension and an excess of X in the other.
... by: Prasolov V.
I've got new ideas for me from this site. Thanks. But you would have more simple methods, and then last example would disappear, such as "Perfect 3-3-3 Swordfish". You have many hard strategies but you have little simple methods. It is not logical.
... by: JK
Very good explanation, but could you add some more examples including the other possible Swordfish formats, 3-2-1 etc?
... by: lec
Re: Swordfish strategy page formatting - the characters in yellow on print version of web page are printing in a light yellow, making them nearly invisible. They are not formatted the way yellow characters on your other strategy pages are (dark blue with yellow highlighting). Nit-picky, I know. (I'll save the kudo until I've actually read the pages, but predict that you deserve many. Hope this makes sense; I'm wiped at the moment, and apologize for not hunting down appropriate address for this comment.)
... by: p davis
my comment refers to Jef's mixed Box/Row example:
any wrapped AIC chain eg.
{a = b - c = d - e = f} - a implies a 'fish'. But as far as spotting patterns and associated eliminations (swordfish in rows, eliminations in columns) it doesn't seem particularly useful, except in theory to extend the definition of SwordFish'.
Your example is:
{r9c3 = r9c4 - r78c6 = r23c6 - r1c45 = r1c3} - r9c3.
this wrapped AIC chain eliminates all non-fish candidates in columns 345.
It's just a structural coincidence that the eliminations all occur in those columns here (so I guess you could technically call the pattern a swordfish).
BTW: a Finned X-Wing is a 2 string Kite is a simple AIC chain:
a = b - c = d, where the geometry of the chain is constrained to a rectangle with a 'group' node in one corner.
... by: Trev
If you had a swordfish with a single cell in it's row (i.e. X-X-1), wouldn't that single cell be a hidden single and therefore you wouldn't need to use the swordfish strategy?
Awesome site by the way!
Andrew Stuart writes: Its not about finding the solution to any one part of the sword-fish itself, its about eliminating candidates outside the swordfish. The '1' in the formation would be a given solution yes, for that cell: we are just reusing it to get something else.
... by: CS VIDYASAGAR
An excellent exposition of really advanced and difficult techniqe which many find it difficult to understand. You explained in simple and easily conprehendible manner. Thanks. Now I am confident of solving extremely difficult Sudoku puzzles using sword fish technique.
... by: jef
A Swordfish is not limited to rows and columns, also boxes can be involved:
. . x|x x .|. . .
. . .|. . .|. . .
. . .|. . .|. . .
-----+-----+-----
. . .|x . .|. . .
. . .|. x .|. . .
. . .|. . .|. . .
-----+-----+-----
. . .|. . .|. . .
. . .|. . .|. . .
. . x|x . .|. . .
Swordfish row 1, box[2,2] and row 9.
Is your solver finding this pattern?
Have you examples of this pattern?
Kind regards,
Jef
PS I totally agree with your remarks on J.F. Crook's paper, nothing new and not a real solution.
http://users.telenet.be/vandenberghe.jef/sudoku/
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